Actually, i think kudzu is considered a nitrogen fixer. it’s technically a legume.
although strawberries generally prefer crappy soil, in my experience. they prefer an acid soil, so mulching with those weeds you pulled would be a good start.
but yeah. leave whatever you can identify. but makes sure you give the strawberries a chance to breath a bit. red clover is generally thought of as a nitrogen fixer as well, although to such a small degree that the effects either way are very minimal. the clover flowers themselves make a very good snack, or cup of tea. it is usually included in whatever ‘male tonics’ blends they sell at the store, and supposedly boosts your ‘fertility’ if your looking for that kind of thing.